With modern internal combustion engines, there are commonly used catalytic converters in order to keep the amount of harmful substances in the exhaust gas as low as possible. The efficiency of the converter crucially depends on the fact that the converter is at its operating temperature. This temperature lies above 250° C. with the materials that are common at present. So that the converter reaches its operating temperature after a cold start of the internal combustion engine in the shortest possible time, various ways have been proposed in prior art, for instance by arranging it as close as possible to the internal combustion engine, so that the exhaust gas hardly cools down before it reaches the converter and can heat the latter up. However, the heating up of the converter which is rapidly achieved in this manner necessarily involves the risk of the converter becoming overheated if the internal combustion engine is operated at high power for a longer time or at full load. The exhaust gas which then will enter the exhaust gas chamber with high temperature can in fact only cool down very little before it reaches the converter. A further disadvantage is that with high temperatures the converter operates outside its optimum performance range and the catalytic action is diminished. Moreover, costly materials and expensive constructions are necessary due to the high temperatures. Hitherto, materials such as Pt, Rh and Pd (typical materials in a conventional three-way converter) are used in the converters. These materials serve for reducing the emission of CO, HC and NOx. The materials employed in the converters are additionally very costly and the converter is so heavily stressed through an operation outside its working temperature range—in which it has its optimum catalytic effect—that it would age prematurely. In order to exclude this, additional fuel serving for cooling the exhaust gas is injected at present when there are high operating temperatures. This, however, significantly increases the consumption with high load.